where \(J_i\)  and \(P_i\)  are the generators of Lorentz transformation and translation respectively [1]}, [2]} .

According to our agreement of dimension assignment, \({\bf e}\)  is with dimension of length and \({\bf A}\) , thus \(F\) , is dimensionless.

Explicitly,
\(S_{\text{CS}}[{\bf e}, {\bf A}]= \frac{k}{4\pi \ell _{\text{p}}}\left[\int _{{\mathcal {M}}} \text{Tr}\left[ {\bf e}\wedge F({\bf A}) \right]+ \int _{\partial {\mathcal {M}}} \text{Tr}\left[ {\bf e}\wedge {\bf A}\right]\right]\,.\) 
